Heat olive oil in a large pot over medium heat. Add chopped onion and cook until translucent, about 5 minutes.
Add minced garlic and cook for another minute.
Stir in pumpkin puree, vegetable broth, coconut milk, cinnamon, nutmeg, salt, and black pepper. Bring to a boil, then reduce heat and simmer for 20 minutes.
Use a blender to puree the soup until smooth. Adjust seasoning if needed.